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Introduction to Decision-Making Under Certainty

Overview of the Course

• The session is introduced by Vladimir Georgievich Ignatiev from Kazan Cooperative Institute, focusing on decision-making theory and risk management.

• Decisions are made under certainty when a manager can accurately determine the outcome of each alternative solution available in a situation.

Characteristics of Decisions Under Certainty

• The level of uncertainty in decision-making depends on external factors; it increases with a solid legal framework that limits alternatives.

• Absolute certainty in decision-making is unattainable; however, near-certain situations exist, such as investing undistributed profits in government securities.

Linear Programming Models

Application of Linear Programming

• Linear programming models exemplify decision-making under certainty, applicable when alternative solutions can be linked through precise linear functions.

• Complete information about all alternatives allows for quantitative assessment where attractiveness is proportional to numerical evaluations.

Importance of Criteria Weights

• Each criterion's importance varies; some influence decisions more than others. This importance is quantified as weights (wj).

• Weights can be determined by experts or set within linear programming models. Maximization tasks require calculating utility functions for optimal decisions.

Example Scenario: Choosing a Service Company

Decision-Making Process

• A director evaluates four service companies (A, B, C, D), considering criteria like cost, warranty obligations, and overhead expenses.

• Financial conditions are weighted most heavily (w1 = 0.8), followed by reliability and reputation (w2 = 0.5), and response speed (w3 = 0.3).

Utility Function Calculation

• Utility functions for each alternative are calculated based on qualitative assessments using a ten-point scale.

• Results indicate that company B has the highest utility function value, making it the most attractive option for contract signing.

Normalization Methods in Decision-Making

Addressing Different Measurement Units

• When criteria have different dimensions (e.g., monetary vs. time), normalization methods are necessary to create comparable metrics.

Normalization Techniques Explained

• One common method involves adjusting scores so they fit into a dimensionless scale through procedures that standardize measurements across criteria.

Example of Normalization Formula

• For maximization scenarios: normalized score = (score - minimum score)/(maximum score - minimum score). For minimization: adjusted accordingly to reflect lower values as better outcomes.

Matrix Normalization and Utility Function Calculation

Overview of Matrix Normalization

• The process involves subtracting each element in a column from the maximum element of that column, followed by dividing the result by the difference between the maximum and minimum elements. This is crucial for normalizing data to ensure independence.

• The utility function for each alternative is calculated using normalized attractiveness scores, where alternatives are rated on a scale from 0 to 1 based on their appeal relative to others.

Example Scenario: Office Space Selection

• A cellular company evaluates several office space options in a city, including locations such as downtown, park area, industrial zone, and market district.

• Key criteria for evaluation include rent price, space area, client accessibility, and condition of premises. These criteria are assessed using a ten-point scoring system presented in a table format.

Normalization Process

• For rent (the first criterion), normalization is performed by taking the maximum rent (130) and subtracting it from each rent value before dividing by the range (130 - 65).

• Similar normalization steps are applied to other criteria like area size. The resulting normalized matrix reflects these calculations visually in tabular form.

Final Evaluation of Alternatives

• After applying weights to utility functions based on normalized scores, alternatives receive final utility values:

• Alternative A (downtown): 15.5

• Alternative B: 14

• Alternative C: 17.6

• Alternative D: 15.44

• The highest utility score indicates that Alternative A (downtown location) is deemed most attractive for selection based on this analysis.